Concise Adaptive Fuzzy Control of Nonlinearly Parameterized and Periodically Time-varying Systems via Small Gain Theory

다국어 초록 (Multilingual Abstract)

This study is concerned with robust adaptive fuzzy stabilization of the nonlinearly parameterized andperiodically time-varying system with known period of the parameterized disturbance. In this note, a novel uncertaintydelivering approach is developed to overcome the problems: “the initial evident oscillating error”, “explosionof complexity” and “curse of dimensionality” from the root causes that are common in the current literatures onapproximation-based algorithms. Furthermore, a novel adaptive fuzzy control scheme is proposed with advantagesof concise structure and easy-to-implementation in practical engineering. Only one fuzzy type approximator isintroduced to compensate uncertainties of the whole system in the scheme. Based on small gain theory, all signalsof the composite closed-loop system are guaranteed to be uniformly ultimately bounded. Finally, three simulationexperiments are presented to demonstrate the effectiveness of our results.

참고문헌 (Reference)

1 M. M. Polycarpou, "Stable adaptive tracking of uncertain systems using nonlinearly parameterized on-line approximators" 70 (70): 363-384, 1998

2 M. M. Polycarpou, "Stable adaptive neural control scheme for nonlinear systems" 41 (41): 447-450, 1996

3 S. S. Ge, "Stable Adaptive Neural Network Control" Springer 2001

4 T. Perez, "Ship roll damping control" 36 (36): 129-147, 2012

5 Y. P. Tian, "Robust learning control for a class of nonlinear systems with periodic and aperiodic uncertainties" 39 (39): 1957-1966, 2003

6 Y. J. Liu, "Robust adaptive tracking control for nonlinearly systems based on bounds of fuzzy approximation parameters" 40 (40): 170-184, 2010

7 Y. S. Yang, "Robust adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems via small-gain approach" 170 (170): 211-234, 2005

8 S. Hara, "Repetitive control system : a new type servo system for periodic exogenous signals" 33 (33): 659-668, 1988

9 S. I. Han, "Recurrent fuzzy neural network backstepping control for the prescribed output tracking performance of nonlinear dynamic systems" 53 (53): 33-43, 2014

10 S. K. Pradhan, "Real-time adaptive control of a flexible manipulator using reinforcement learning" 9 (9): 237-249, 2012

11 B. Chen, "Novel adaptive neural control design for nonlinear MIMO time-delay systems" 45 (45): 1554-1560, 2009

12 M. Krstic, "Nonlinear and Adaptive Control Design" Wiley 1995

13 D. Wang, "Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form" 16 (16): 195-202, 2005

14 R. Huang, "Lyapunov stability of economically oriented NMPC for cyclic processes" 21 (21): 501-509, 2011

15 W. Guan, "Integrated rudder/fin concise control based on frequency domain analysis" 11 (11): 3841-3854, 2013

16 T. I. Fossen, "Handbook of Marine Craft Hydrodynamics and Motion Control" Wiley 2011

17 Shu-Ping He, "Fault Estimation for T-S Fuzzy Markovian Jumping Systems based on the Adaptive Observer" 제어·로봇·시스템학회 12 (12): 977-985, 2014

18 D. Swaroop, "Dynamic surface control for a class of nonlinear systems" 45 (45): 1893-1900, 2000

19 S. S. Ge, "Direct adaptive NN control of a class of nonlinear systems" 13 (13): 214-221, 2002

20 M. S. Kahkeshi, "Design of adaptive fuzzy wavelet neural sliding mode controller for uncertain nonlinear systems" 52 (52): 342-350, 2013

21 T. S. Li, "Decentralized adaptive neural control of nonlinear interconnected large-scale systems with unknown time delays and input saturation" 74 (74): 2277-2283, 2011

22 M. Tomizuka, "Dealing with periodic disturbances in controls of mechanical systems" 32 (32): 193-199, 2008

23 W. Guan, "CGSA control methodology applied to ship integrated rudder and fin stabilization system" 253-255 (253-255): 2080-2085, 2013

24 S. S. Ge, "Approximation-based control of nonlinear MIMO time-delay systems" 43 (43): 31-43, 2007

25 M. -C. Fang, "Applying the PD controller on the roll reduction and tracking keeping for the ship advancing in waves" 54 (54): 13-25, 2012

26 C. Wang, "An ISSmodular approach for adaptive neural control of purefeedback systems" 42 (42): 723-731, 2006

27 W. S. Chen, "Adaptive tracking for periodically time-varying and nonlinearly parameterized systems using multilayer neural networks" 21 (21): 345-351, 2010

28 J. Na, "Adaptive neural network predictive control for nonlinear pure feedback systems with input delay" 22 (22): 194-206, 2012

29 T. S. Li, "Adaptive neural control of nonlinear MIMO systems with unknown time delays" 78 (78): 83-88, 2012

30 D. W. C. Ho, "Adaptive neural control for a class of nonlinearly parametric time-delay systems" 16 (16): 625-635, 2005

31 S. Liuzzo, "Adaptive learning control of nonlinear systems by output error feedback" 52 (52): 1232-1248, 2007

32 B. Yoo, "Adaptive fuzzy sliding mode control of nonlinear system" 6 (6): 315-321, 1998

33 B. Chen, "Adaptive fuzzy control of a class of nonlinear systems by fuzzy approximation approach" 20 (20): 1012-1021, 2012

34 P. P. Yip, "Adaptive dynamic surface control : a simplified algorithm for adaptive backstepping control of nonlinear systems" 71 (71): 959-979, 1998

35 G. Sun, "Adaptive control based on single neural network approximation for nonlinear pure feedback systems" 6 (6): 2387-2396, 2012

36 W. S. Chen, "Adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances" 18 (18): 674-685, 2010

37 W. S. Chen, "Adaptive backstepping dynamic surface control for systems with periodic disturbances using neural networks" 3 (3): 1383-1394, 2009

38 M. Chen, "Adaptive NN tracking control of overactuated ocean surface vessels" 548-552, 2010

39 Y. S. Yang, "Adaptive H¥ tracking control for a class of uncertain nonlinear systems using radialbasis-function neural networks" 70 (70): 932-941, 2007

40 Yong-Qing Fan, "Adaptive Fuzzy Control with Compressors and Limiters for a Class of Uncertain Nonlinear Systems" 제어·로봇·시스템학회 11 (11): 624-629, 2013

41 T. -S. Li, "A novel robust adaptive-fuzzy-tracking control for a class of nonlinear multi-input/multi-output systems" 18 (18): 150-160, 2008

42 Z. -P. Jiang, "A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems" 32 (32): 1211-1215, 1996

43 T. S. Li, "A DSC approach to robust adaptive NN tracking control for strictfeedback nonlinear systems" 40 (40): 915-927, 2010